Fuzzy reasoning rules in accordance with a modus ponens inference format generally are written in an "If, . . . , then . . . " format, and are accompanied by membership functions. In order to set these rules, it is necessary to set (or register) the membership functions.
Let input variables be expressed by I.sub.1 -I.sub.n, and output variables by O.sub.1 -O.sub.m. Membership functions often are represented by labels NL, NM, NS, ZR, PS, PM, PL, which express the characterizing features of the functions. Here N represents negative, and P, L, M, S, and ZR represent positive, large, medium, small and zero, respectively. For example, NL, which stands for "negative large", represents a fuzzy see (membership function) in which the particular concept is defined by the linguistic information "a negative, large value". In addition, PS represents a positive, small value, and ZR represents approximately zero. The items of linguistic information which represent the characterizing features of these membership functions are referred to as "labels" hereinbelow.
One method of setting membership functions in the programming of reasoning rules according to the prior art is to define membership functions, with regard to respective ones of the labels used, for every input variable and output variable. Specifically, seven types of membership functions NLIp, NMIp, . . . , PLIp are defined for each input variable Ip (p=1-n), and seven types of membership functions NL.sub.Oq, NM.sub.Oq, . . . , PL.sub.Oq are defined for each output variable O.sub.q (q=1-m). The advantage of this method is that membership functions of desired forms can be defined for every input variable, output variable and label, and it is possible to finely adjust each one. A disadvantage which can be mentioned is that a large capacity memory is required as the membership-function memory. For example, if the region of a variable of one membership function is divided into 256 portions and a function value is represented by eight bits (256 stages) for every subdivision of the variable resulting from division, then a capacity of 2 Kbits (256.times.8=2,048) per membership function will be required. If the number of types of input variables is 10 (n=10), the number of types of output variables is 2 (m=2) and seven types of membership functions are set for each of the input and output variables, then the memory capacity necessary will be 10.times.2.times.(2 K).times.7=280 Kbits. This method involves other problems as well, such as the need to set a large number of membership functions (20.times.7=140 types), which is laborious and troublesome.
Another method is to use the same membership functions for all of the input and output variables. Memory capacity required in accordance with this method is only (2 K).times.7=14 Kbits, and the setting of seven types of membership functions will suffice. However, since the forms of the membership functions are already decided, a drawback is that a fine adjustment cannot be made.
Still another method is to create the necessary membership functions in advance and assign different codes (numbers) to respective ones of these membership functions. For example, in a case where 27 types of membership functions are necessary, these are created and stored in memory, and identification codes are assigned to them in the manner MF.sub.1, MF.sub.2, . . . , MF.sub.27. As a result, the required capacity of the memory can be reduced to the minimum. In accordance with this method, rules are expressed using the identification numbers, as follows:
If I.sub.1 =MF.sub.5, I.sub.2 =MF.sub.13, . . . , and I.sub.n =MF.sub.6, then O.sub.1 =MF.sub.9
According to this method, labels cannot be used in the rules in order to designate the membership functions. Therefore, a problem which arises is that the description of rules is very difficult to understand.
On the other hand, in the application of a fuzzy reasoning apparatus, how to set inference rules and membership functions that are appropriate for the controlled system is an important problem. In addition, analyzing what role rules and membership functions, once they have been set, play in fuzzy reasoning, as well as how a plurality of set rules and membership functions are interrelated, is an essential matter in order to refine upon and improve fuzzy reasoning control.
However, research concerning the applications of fuzzy reasoning has only just begun, and the state of the art is such that adequate research has not yet been carried out.